Moving horizon state estimation for constrained discrete-time systems by using fast descent methods

Fast moving horizon state estimation for constrained discrete-time systems is investigated through an approach based on an incomplete optimization at each time step. In particular, only few iterations of the gradient, conjugate gradient, and Newton descent methods are executed. Constraints on the state variables are explicitly considered by exploiting the "dead time" between two consecutive time steps, where a projection requiring the minimization of a distance function is performed. Instead, a simpler line search is computed on line that consists in searching for a state estimate satisfying the constraints by solving a one-dimensional optimization. Stability conditions for the estimation error are derived. The proposed approach is well-suited to being applied for state estimation of rapidly-evolving constrained systems, as confirmed by simulations in comparison with the application of the online "full" projection at each time step.